My dd was defiantly doing the fake cough at 5 months! She would always follow with a smile or if I said are you alright she would do it more such a good age!!
At 16 months she still does it but she now runs to get my spew bucket and coughs into that!! She has been watching mummy too much
Even if it is a real cough if he doesn't have temps or seems sick I wouldn't worry about it, it's not like he can have cough medicine... Although I did read that coughing can be an early sign of asthma... Don't know if that's true though!